Assertion (A): Sum of first 15 terms of 2 + 5 + 8 … is 345

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Q.
Assertion (A): Sum of first 15 terms of 2 + 5 + 8 … is 345.

Reason (R): Sum of first n terms in an AP is given by the formula:

$S_{n} = n / 2 [2 a + (n - 1) d]$

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(1)

We have AP = 2 + 5 + 8 + …

Here, a = 2, d = 5 – 2 = 3, n = 15

$S_{15} = 15 / 2 (2 \times 2 + 14 \times 3) = 15 / 2 (4 + 42) = 15 / 2 \times 46 = 15 \times 23 = 345$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Solution

Q.
Assertion (A): Sum of first 15 terms of 2 + 5 + 8 … is 345.

Reason (R): Sum of first n terms in an AP is given by the formula:

$S_{n} = n / 2 [2 a + (n - 1) d]$

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans.
(1)

We have AP = 2 + 5 + 8 + …

Here, a = 2, d = 5 – 2 = 3, n = 15

$S_{15} = 15 / 2 (2 \times 2 + 14 \times 3) = 15 / 2 (4 + 42) = 15 / 2 \times 46 = 15 \times 23 = 345$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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Solution

Q. Assertion (A): Sum of first 15 terms of 2 + 5 + 8 … is 345. Reason (R): Sum of first n terms in an AP is given by the formula: Sn=n/2[2a+(n-1)d]

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A.

3 A is true, but R is false.

4 A is false, but R is true.

Ans. (1) We have AP = 2 + 5 + 8 + … Here, a = 2, d = 5 – 2 = 3, n = 15 S15=15/2(2×2+14×3)=15/2(4+42)=15/2×46=15×23=345 Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

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Q.
Assertion (A): Sum of first 15 terms of 2 + 5 + 8 … is 345.

Reason (R): Sum of first n terms in an AP is given by the formula:

$S_{n} = n / 2 [2 a + (n - 1) d]$

Ans.
(1)

We have AP = 2 + 5 + 8 + …

Here, a = 2, d = 5 – 2 = 3, n = 15

$S_{15} = 15 / 2 (2 \times 2 + 14 \times 3) = 15 / 2 (4 + 42) = 15 / 2 \times 46 = 15 \times 23 = 345$

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).